Properties of air and water vapour mixtures

The most important thing for the student of psychrometry to understand from the outset is that the working fluid under study is a mixture of two different gaseous substances.

One of these, dry air, is itself a mixture of gases, and the other, water vapour, is steam in the saturated or superheated condition. Some of the most important standards are,

- Density of air, ρair 1,296 kg/m³ for dry air at 101325 Pa and 0 °C.

- Density of water, ρwater 999,9 kg/m³ at 0 °C and - Barometric pressure, p_atm 101325 Pa in 0 °C. [3][10]

3.1.1 The general gas law The general gas law is expressed as:

T temperature of the gas in K.

Avogadro´s hypothesis argues that equal volumes of all gases at the same temperature and pressure contain the same number of molecules. Accepting this and taking as the unit of mass the kilomole (kmol), a mass in kilograms numerically equal to the molecular mass of the gas, a value for the universal gas constant can be established:

T constant, Ro, is determined

K

Specific gas constants of dry air and steam are expressed as

K

where Ma and Ms are molecular masses of dry air and steam. A suitable transposition of the general gas law gives expressions for density, pressure and volume. [10][15]

3.1.2 Dalton's law of partial pressure Dalton’s law may be stated as follows:

If a mixture of gases occupies a given volume at a given temperature, the total pressure exerted by the mixture equals the sum of the pressures of the components, each being considered at the same volume and temperature.

It is possible to show that if Dalton's law holds, each component of the mixture obeys the general gas law. As a consequence, it is sometimes more convenient to re-express the law in two parts: [3][10]

(1) The pressure exerted by each gas in a mixture of gases is independent of the presence of the other gases, and

(2) The total pressure exerted by a mixture of gases equals the sum of the partial pressures.

3.1.3 Saturation vapour pressure

There are two requirements for the evaporation of liquid water to occur:

- Thermal energy must be supplied to the water, and

- The vapour pressure of the liquid must be greater than that of the steam in the environment.

These statements need some explanation.

Molecules in the liquid state are comparatively close to each other. They are nearer to each other than are the molecules in a gas and are less strongly bound together than those in a solid. The three states of matter are further distinguished by the extent to which an individual molecule may move. At a given temperature, a gas consists of molecules which have high individual velocities and which are arranged in a random fashion. A liquid at the same temperature is composed of molecules, the freedom of movement of which is much less, owing to the restraining effect which neighbouring molecules have on each other, by virtue of their comparative proximity. An individual molecule, therefore, has less kinetic energy if it is in the liquid state than it has in the gaseous state. Modern thought is that the arrangement of molecules in a liquid is not entirely random as in a gas, but that it is not as regular as it is in most, if not all, solids.

It is evident that if the individual molecular kinetic energies are greater in the gaseous state, then energy must be given to a liquid when it is changing to the gaseous phase. This explains the first stated requirement for evaporation.

As regards the second requirement, the situation is clarified if one considers the boundary between a vapour and its liquid. Only at this boundary can a transfer of molecules between the liquid and the gas occur. Molecules at the surface have a kinetic energy, which has a value related to the temperature of the liquid. Molecules within the body of the gas also have a kinetic energy, which is a function of the temperature of the gas. Those gaseous molecules near the surface of the liquid will, from time to time, tend to hit the surface of the liquid, some of them staying there. Molecules within the liquid and near to its surface will, from time to time, also tend to leave the liquid and enter the gas, some of them staying there.

It has been found that water in an ambient gas which is not pure steam but a mixture of dry air and steam, behaves in a similar fashion, and that for most practical purposes the relationship between saturation temperature and saturation pressure is the same for liquid water in contact only with steam. One concludes from this a very important fact:

saturation vapour pressure depends solely upon temperature. [10]

3.1.4 Moisture content and relative humidity

Moisture content is defined as the mass of water vapour in kg, which is associated with one kilogram of dry air in an air-water vapour mixture.

a s

m m m content

Moisture  (3.1.5)

Relative humidity is a term used to describe the amount of water vapour in a mixture of air and water vapour. It is defined as the ratio of the partial pressure of water vapour in the air-water mixture to the saturated vapour pressure of water at those conditions. The relative humidity of air depends not only on temperature but also on pressure of the system of interest. Relative humidity is often used instead of absolute humidity in situations where the rate of water evaporation is important, as it takes into account the variation in saturated vapour pressure. [4]

Relative humidity is defined as

%

100



ss s

p Φ p ratio

Humidity (3.1.6)

where ps is a pressure of water vapour and pss is the saturation vapour pressure

3.1.5 Dew point and specific volume of the mixture

The dew point is the temperature to which a given parcel of humid air must be cooled, at constant barometric pressure, for water vapour condense into liquid water. The condensed water is called dew when it forms on a solid surface. The dew point is a saturation temperature.

The dew point is associated with relative humidity. A high relative humidity indicates that the dew point is closer to the current air temperature. Relative humidity of 100 % indicates the dew point is equal to the current temperature and the air is maximally saturated with water. When the dew point remains constant and temperature increases, relative humidity will decreases. [5]

Specific volume of the mixture is the volume in m³ of one kilogram of dry air mixed with water vapour. In the mixture each component occupies the same volume and is at the same temperature, but each exerts its own partial pressure. By Dalton’s law sum of these partial pressures is the total (barometric) pressure of the mixture. The general gas law, may be transposed to express the specific volume:

p T R

V  m  (3.1.7)

This equation could be used to refer to the dry air, or to the water vapour, independently if Dalton’s law is accepted. In doing so, the appropriate values for the mass, specific gas constant and partial pressure of the constituent considered must be used. [10]

3.1.6 Enthalpy of moist and dry air

The enthalpy, h, used in psychrometry is the specific enthalpy of moist air, expressed in kJ/kgdry air, defined by the equation:

g

a g h

h

h   (3.1.8)

where h_a is the enthalpy of dry air, g is the moisture content in kg/kg_{,dry air}, and h_g is the enthalpy of water vapour, both expressed in kJ/kg. An approximate equation for the enthalpy of dry air over the range 0 °C to 60 °C is

026 . 0 007

.

1  

 T

h_a (3.1.9)

and the following equation can be used for the enthalpy of water vapour:

T

h_g 25011.84 (3.1.10)

Equations (3.1.9) and (3.1.10) can now be combined, as typified by equation (3.1.8), to give an approximate expression for the enthalpy of humid air:

) 1.84 (2501 0.026)

-(1.007 T g T

h      (3.1.11)

Equation (3.1.11) is valid at a barometric pressure (101325 Pa). [10]

In document Calculation Tool for Fan Coil Unit (sivua 14-18)